¿Cómo se desarrolla el siguiente ejercicio?

<img src="https://tex.z-dn.net/?f=%7B%5Clog%20_2%5Cleft%28105%5Cright%29%7D%3Dy" />

Utilzar la propiedad de antilogartitmo :

<img src="https://tex.z-dn.net/?f=2%5E%7B%5Clog%20_2%5Cleft%28105%5Cright%29%7D%3D%202%5E%7By%7D" />

<img src="https://tex.z-dn.net/?f=%5Cmathrm%7BAplicar%5C%3Alas%5C%3Apropiedades%5C%3Ade%5C%3Alos%5C%3Alogaritmos%7D%3A%5Cquad%20%5C%3Aa%5E%7B%5Clog%20_a%5Cleft%28b%5Cright%29%7D%3Db" />

<img src="https://tex.z-dn.net/?f=105%3D2%5Ey" />

Aplicar logaritmos a ambos miembros :

<img src="https://tex.z-dn.net/?f=%5Clog%20_%7B10%7D%5Cleft%28105%5Cright%29%3D%5Clog%20_%7B10%7D%5Cleft%282%5Ey%5Cright%29" />

<img src="https://tex.z-dn.net/?f=%5Cmathrm%7BAplicar%5C%3Alas%5C%3Apropiedades%5C%3Ade%5C%3Alos%5C%3Alogaritmos%7D%5C%3A%5Clog%20_a%5Cleft%28x%5Eb%5Cright%29%3Db%5Ccdot%20%5Clog%20_a%5Cleft%28x%5Cright%29" />

<img src="https://tex.z-dn.net/?f=%5Clog%20_%7B10%7D%5Cleft%28105%5Cright%29%3Dy%5Clog%20_%7B10%7D%5Cleft%282%5Cright%29" />

Despejar y :

<img src="https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B%5Clog%20_%7B10%7D%5Cleft%28105%5Cright%29%7D%7B%5Clog%20_%7B10%7D%5Cleft%282%5Cright%29%7D%20" />

<img src="https://tex.z-dn.net/?f=%5Cleft%28%5Cmathrm%7BDecimal%3A%5Cquad%20%7Dy%3D6.71425%5Cdots%20%5Cright%29" />.